Feigenbaum diagram

In Fig.3 the analogous Feigenbaum diagram is presented, which illustrates the character of dynamics of the system under consideration as a function of the division of stream of feed degree q. 

Figure 2.15. Feigenbaum diagram if a reaction parameter (e.g. combination of concentrations and temperature) deviates sufficiently far from equilibrium conditions, the rate of the reaction may start to oscillate between several levels. At high deviations from equilibrium the system may behave chaotically.

The reader will have noticed by now that we have introduced many new terms such as Hopf bifurcation point, static limit point, Feigenbaum sequence, Poincare diagram and so forth in this section. These terms have never occurred before in this book and they were left undefined in this section. 

The bifurcation diagram of Figure 2.15 is often referred to as the Feigenbaum route to chaos. It applies also to reactions such as CO + O2 and NO + H2 on platinum, as Figure 2.16 shows. The single period oscillation between two states corresponds to point Xi in Figure 2.15, the double period oscillation between four states at A = A2, a four period oscillation between eight states (A3) and the aperiodic, unpredictable oscillation of an essentially chaotic system. 

---